Notes and Reference


Calculus: Early Transcendentals 8th Edition by James Stewart Notes

Calculus: Early Transcendentals 8th Edition by James Stewart Reference Pages

1 Functions and Models


1.1 Four Ways to Represent a Function

1.2 Mathematical Models

1.3 New Functions from Old Functions

1.4 Exponential Functions

1.5 Inverse Functions and Logarithms

2 Limits and Derivatives


2.1 The Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 The Precise Definition of a Limit

2.5 Continuity

2.6 Limits at Infinity

2.7 Derivatives and Rates of Change

2.8 The Derivative as a Function

3 Differentiation Rules


3.1 Derivatives of Polynomials and Exponentials

3.2 The Product and Quotient Rules

3.3 Derivatives of Trigonometric Functions

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Logarithmic Functions

3.7 Rates of Change in the Sciences

3.8 Exponential Growth and Decay

3.9 Related Rates

3.10 Linear Approximations and Differentials

3.11 Hyperbolic Functions

4 Applications of Differentiation


4.1 Maximum and Minimum Values

4.2 The Mean Value Theorem

4.3 Derivatives and the Shape of a Graph

4.4 Indeterminate Forms and l'Hospital's Rule

4.5 Summary of Curve Sketching

4.6 Graphing with Calculus and Calculators

4.7 Optimization Problems

4.8 Newton's Method

4.9 Antiderivatives

5 Integrals


5.1 Areas and Distances

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Net Change Theorem

5.5 The Substitution Rule

6 Applications of Integration


6.1 Areas Between Curves

6.2 Volumes

6.3 Volumes by Cylindrical Shells

6.4 Work

6.5 Average Value of a Function

7 Techniques of Integration


7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitution

7.4 Integration by Partial Fractions

7.5 Strategy for Integration

7.6 Integration Using Tables and Computer Algebra Systems

7.7 Approximate Integration

7.8 Improper Integrals

8 Further Applications of Integration


8.1 Arc Length

8.2 Area of a Surface of Revolution

8.3 Applications to Physics and Engineering

8.4 Applications to Economics and Biology

8.5 Probability

9 Differential Equations


9.1 Modeling with Differential Equations

9.2 Direction Fields and Euler's Method

9.3 Separable Equations

9.4 Models for Population Growth

9.5 Linear Equations

9.6 Predator-Prey Systems

10 Parametric Equations and Polar Coordinates


10.1 Curves Defined by Parametric Equations

10.2 Calculus with Parametric Curves

10.3 Polar Coordinates

10.4 Areas and Lengths in Polar Coordinates

10.5 Conic Sections

10.6 Conic Sections in Polar Coordinates

11 Infinite Sequences and Series


11.1 Sequences

11.2 Series

11.3 The Integral Test and Estimates of Sums

11.4 The Comparison Tests

11.5 Alternating Series

11.6 Absolute Convergence, Ratio and Root Tests

11.7 Strategy for Testing Series

11.8 Power Series

11.9 Representations of Functions as Power Series

11.10 Taylor and Maclaurin Series

11.11 Applications of Taylor Polynomials

12 Vectors and the Geometry of Space


12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Equations of Lines and Planes

12.6 Cylinders and Quadric Surfaces

13 Vector Functions


13.1 Vector Functions and Space Curves

13.2 Vector Function Derivatives and Integrals

13.3 Arc Length and Curvature

13.4 Motion in Space

14 Partial Derivatives


14.1 Functions of Several Variables

14.2 Limits and Continuity

14.3 Partial Derivatives

14.4 Tangent Planes and Linear Approximations

14.5 The Chain Rule

14.6 Directional Derivatives and the Gradient

14.7 Maximum and Minimum Values

14.8 Lagrange Multipliers

15 Multiple Integrals


15.1 Double Integrals over Rectangles

15.2 Double Integrals over General Regions

15.3 Double Integrals in Polar Coordinates

15.4 Applications of Double Integrals

15.5 Surface Area

15.6 Triple Integrals

15.7 Integrals in Cylindrical Coordinates

15.8 Integrals in Spherical Coordinates

15.9 Change of Variables in Multiple Integrals

16 Vector Calculus


16.1 Vector Fields

16.2 Line Integrals

16.3 Fundamental Theorem for Line Integrals

16.4 Green's Theorem

16.5 Curl and Divergence

16.6 Parametric Surfaces and Their Areas

16.7 Surface Integrals

16.8 Stokes' Theorem

16.9 The Divergence Theorem

17 Second-Order Differential Equations


17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications of Second-Order Differential Equations

17.4 Series Solutions